Adaptive Modified Newton algorithm for multiple frequencies estimation

In this paper, we study the problem of adaptive retrieval of multiple sinusoids in white noise. It is shown that frequency estimation problem can be reformulated as an unconstrained optimization problem. Based on the proposed cost function, we derive a new adaptive quasi-Newton algorithm for tracking frequencies by approximating Hessian matrix appropriately, which not only significantly reduces the computation complexity, but also makes the proposed algorithm more numerically robust due to positive definiteness of the Hessian matrix no matter if it is implemented as infinite or finite precision. Simulation results show that the proposed adaptive frequency estimation algorithm has fast convergence and excellent tracking capability in nonstationary environment.